To calculate the probability of drawing two Kings in a row without replacement, we need to follow these steps:
1. Determine the Probability of Drawing the First King:
There are 4 Kings in a standard deck of 52 cards. Thus, the probability of drawing the first King is:
[tex]\[ \text{Probability of first King} = \frac{4}{52} \][/tex]
2. Determine the Probability of Drawing the Second King:
Once the first King is drawn, there are only 3 Kings left in the remaining 51 cards. Hence, the probability of drawing a King from the remaining cards is:
[tex]\[ \text{Probability of second King} = \frac{3}{51} \][/tex]
3. Calculate the Combined Probability:
The combined probability of both events occurring (drawing two Kings in a row) is found by multiplying the probabilities of each individual event:
[tex]\[ \text{Combined Probability} = \text{Probability of first King} \times \text{Probability of second King} \][/tex]
[tex]\[ \text{Combined Probability} = \left( \frac{4}{52} \right) \times \left( \frac{3}{51} \right) \][/tex]
From the given numerical results:
[tex]\[ \text{Probability of first King} = 0.07692307692307693 \][/tex]
[tex]\[ \text{Probability of second King} = 0.058823529411764705 \][/tex]
[tex]\[ \text{Combined Probability} = 0.004524886877828055 \][/tex]
So, the combined probability of drawing two Kings in a row, without replacement, is approximately 0.0045, which can also be expressed as 0.45%.
Among the options provided, none of them match exactly. However, observe that the numerical value from the calculations guides us to the correct understanding. Thus, the correct option based on the above solution does not appear to match the exact probability calculated. The correct probability should indeed be approximately 0.0045 or 0.45%, which isn't represented exactly by the options given.
